In modern telecommunication systems, such as mobile radio and satellite communication systems, communication signals are typically processed in digital form. Digital processing of communication signals provides a number of advantages, as digital representations of signals can be easily stored, manipulated, encoded, encrypted, etc., by a communication device. Digital processors are used in modern telecommunications devices to perform these complex processing tasks while adhering to reasonable power and size constraints. However, in order to transfer information stored in digital form to another communication device over a communication medium, the digital representation of the signal must first be converted into an analog signal. This conversion process is performed by a digital-to-analog converter (DAC).
FIG. 1 is a block diagram of a transmitter architecture that uses an RF DAC. As discussed below, an RF DAC performs both digital to analog conversion and frequency up-conversion of the resulting analog signal. As shown in FIG. 1, the transmitter includes a processor 10 that generates a stream of digital information to be transmitted, an encoder 12 that encodes the digital information for transmission, and an RF DAC 14 that converts the digital information into an analog signal. A typical DAC operates by generating an output pulse having a voltage level that corresponds to a digital signal value and holding the voltage level for a predetermined time period. This process is referred to as “sample and hold” or “S&H.”
The modulated signal output by the RF DAC 14 is then passed through a bandpass filter 22 having a center frequency corresponding to the frequency of the carrier signal. The filtered signal is then amplified by an amplifier 24 and transmitted using an antenna 20.
The signal output by the encoder 12 may be an oversampled digital signal that represents an analog signal that is to be transmitted by the transmitter. “Sampling” refers to the process of digitizing an analog signal. Sampling of an analog signal is illustrated in FIG. 2A, which is a graph of a signal 30 which is a sine wave that has been sampled at discrete intervals corresponding to a sampling frequency fS=1/TS, where TS is the spacing between samples. The samples 32, which are indicated as dots on FIG. 2A, can be used to reconstruct the signal 30 provided the sampling frequency is at least twice the frequency of the signal 30. The frequency that is one-half the sampling frequency, which represents the highest frequency component of a signal that can be accurately reproduced from a sampled version of the signal, is referred to as the Nyquist frequency. That is fN=fS/2, where fN is the Nyquist frequency and fS is the sampling frequency.
As shown in FIG. 2B, the samples 32 can also correspond to other sine waves, such as the higher frequency sine wave 34 that is superimposed onto the signal 30, even though the higher frequency component of the sine wave 34 did not exist in the original signal 30. This effect is referred to as “aliasing.” The higher frequency sine wave 34 is referred to as an aliased signal or an “image” of the original signal 30.
As shown in FIG. 2C, other aliased signals are generated when the original signal 30 is digitized. These aliased signals appear at frequencies that are related to the frequency f0 of the original signal 30 and the sampling frequency fS. In particular, the aliased signals appear at frequencies that are spaced apart by f0 Hz from multiples of the sampling frequency fS.
A signal is said to be oversampled when it is sampled at a sampling frequency that is more than twice the highest frequency component of the analog signal (i.e. more than twice the Nyquist frequency).
When a digital signal is converted to analog, the aliased images present in the digital signal remain in the analog signal. Before the signal is transmitted, it is desirable to remove unwanted images from the analog signal.